Worldline algorithm by oracle-guided variational autoregressive network

TL;DR

This paper introduces an oracle-guided variational autoregressive network that efficiently samples quantum path integrals with periodic boundary conditions, enabling accurate solutions for quantum spin chains at finite temperatures.

Contribution

It extends variational autoregressive networks to quantum path integrals by incorporating an oracle for nonlocal constraints, allowing rejection-free sampling under periodic boundary conditions.

Findings

Successfully applied to quantum spin chains at finite temperatures.

Achieved efficient computation of thermodynamic quantities.

Enabled handling of larger system sizes and more time slices.

Abstract

The variational autoregressive network is extended to the Euclidean path integral representation of quantum partition function. An essential challenge is adapting the sequential process of sample generation by an autoregressive network to a nonlocal constraint due to the periodic boundary condition in path integral. An add-on oracle is devised for this purpose, which accurately identifies and stalls unviable configurations as soon as they occur. The oracle enables rejection-free sampling conforming to the periodic boundary condition. As a demonstration, the oracle-guided autoregressive network is applied to obtain variational solutions of quantum spin chains at finite temperatures with relatively large system sizes and numbers of time slicing, and to efficiently compute thermodynamic quantities.